# Global Positioning System GPS

W
Shared by:
Categories
Tags
-
Stats
views:
15
posted:
6/8/2012
language:
English
pages:
18
Document Sample

```							Global Positioning Systems
(GPS)
for Precision Farming

An Introduction
The plan
• Introduction to GPS
–   What is GPS
–   How GPS works
–   Differential Correction
–   Integration and application of GPS into PF
systems
Introduction to GPS
• What is GPS
– The Global Positioning System (GPS) is a
constellation of 24 satellites and their ground
stations
– GPS receivers use these satellites as reference
points to calculate positions and time
– Originally known as NAVigation System with
Timing And Ranging (NAVSTAR)
How GPS Works (Six Steps)
1.   Triangulation
2.   Distance
3.   Clocks
4.   Satellite Position
5.   Coordinate system
6.   Errors
Triangulation
• Number of Satellites
–   One distance = sphere
–   Two distances = circle
–   Three distances = two points
–   Four distances = one point
–   Three distances + earths surface = one point
• Locking
– 1,2 satellites - No lock, course time
– 3 Satellites - 2D positioning (Earth’s surface assumed)
– 4 Satellites - 3D positioning (Lat/Lon/Alt)
Triangulation - critical points
• Position is calculated from distance
measurements (ranges) to satellites.
• Mathematically we need four satellite ranges
to determine exact position.
• Three ranges are enough if we reject
ridiculous answers or use other tricks.
• Another range is required for calculation of
time.
Distance
• Distance = Speed x Time ?
– 180 miles = 60 miles per hour x 3 hours
• Speed of radio waves ?
– 186 kmps
• Time
– 0.06 second
• Distance = 186000 mps x 0.06 s
– D = 11,160 miles (11Hr 58 Min period)
• Accuracy (+/- 0.000,000,001 sec) = +/- 1 ns
Distance
• How does a receiver time the signal travel?
– Satellites send a pseudo-random code
• (each sends its own song of 1’s and 0’s)
– Receiver matches its calculated sequence with the
received signal by delaying more or less it’s signal
– The amount of delay = the transit time!
• How does the receiver separate the signals of
each of the satellites?
– Each satellite has it’s own sequence (song)
calculated through a formula
– Formula is conveyed in data from the satellites
Distance - critical points
– Distance to satellites is determined by measuring
signal travel time.
– Assume satellite and GPS receiver generate same
pseudo-random codes at the same time.
– By synchronizing the pseudo-random codes, the
delay in receiving the code can be found.
– Multiply delay time by the speed of light to get
distance
Synchronization
• Satellites timing is extremely accurate.
– precise atomic clocks on board.
• All satellite clocks are synchronized and they
send their codes at a known time
• Ground GPS unit synchronizes its clock with
the satellites
– Four satellites with same time = only one correct
solution for 1. time and 3. distances
• (4 Equations, 4 unknowns)
Synchronization - critical points
• Accurate timing allows distance to satellites to
be measured
• Satellites achieve accurate timing with on-
board atomic clocks.
• Receiver clocks can be accurate because an
extra satellite range measurement can
remove errors.
Where are the satellites?
(ephemeris)
• Satellites are launched into precise orbits
• GPS receivers use an almanac to calculate
accurate positions for the satellites
(ephemeris)
• Almanac is sent from satellites
• US Airforce measures error in ephemeris
(satellite position and speed) when they fly
over C. Springs
• Corrected ephemeris info is sent up to the
satellite
ephemeris - critical points
• Satellite position (ephemeris) must be known
as a reference for range measurements.
• GPS satellite orbits are very predictable.
• Minor variations in their orbits are measured
by the Department of Defense.
• The ephemeris error information is sent to the
satellites, to be transmitted along with the
timing signals.
Coordinate Systems
• ECEF Coordinates
– Latitude/Longitude/Altitude
• Degrees Minutes Seconds (Ag Hall, OSU USA)
– Latitude 360 07’ 29” N
– Longitude 970 04’ 21” W
– Latitude = degrees from equator N or S
– Longitude = degrees from Greenwitch E or W
– Altitude = Meters above reference geoid
• GPS uses WGS84 Ellipsoid (ECEF)
• See: Peter Dana’s Web site
Coordinate Systems
• UTM
–   Cartesian positioning in meters
–   Abbreviation for “Universal Transverse Mercator”
–   Divided into cartesian zones
–   60 wide, 840 North to 800 south
• Reference
– Specifies a starting point for measurement
– Important to account for error between survey
reference and actual lat/lon
Computation of distance along
Longitude

S =R
Lon

R=6,433,000m
   S      Lon

R

31.2 m/s

South
Computation of distance along
Latitude

SLat=R40
R40          

R40=R cos 
25.6 m/s

South
Error Budget
Typical Error in Meters (per satellite)
Standard GPS Differential GPS
Satellite Clocks        1.5                 0
Orbit Errors            2.5                 0
Ionosphere               5                 0.4
Troposphere             0.5                0.2
Multipath               0.6                0.6
SA                      30                  0

Typical Position Accuracy
Horizontal               50                1.3
Vertical                 78                 2
3-D                      93                2.8

```
Related docs
Other docs by tHFDywCb
BIOLOGY 1ST SEMESTER EXAM REVIEW